Answer:
See Below.
Step-by-step explanation:
We are given that ΔAPB and ΔAQC are equilateral triangles.
And we want to prove that PC = BQ.
Since ΔAPB and ΔAQC are equilateral triangles, this means that:
Likewise:
Since they all measure 60°.
Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:
Likewise:
Since ∠QAC ≅ ∠PAB:
And by substitution:
Thus:
Then by SAS Congruence:
And by CPCTC:
Wouldn't it be 12y-2? or is there information you are leaving out?
Answer:
v = 126°
Step-by-step explanation:
Since 54° and u are corresponding angles in parallel lines, they are equal, hence, u = 54°. u and v are Same Side Interior angles. In parallel lines, Same Side Interior angles are supplementary (meaning that they add up to 180°), therefore, v = 180 - u = 180 - 54 = 126°.
Angle-5 and angle-7 are 'vertical angles', so they're equal,
and we can write ...
<u>10x- 9 = 9x</u>
Subtract 9x from each side: x - 9 = 0
Add 9 to each side: <u> x = 9</u>
Now that we know what 'x' is, we can find the size of Angles-5 and -7 .
Angle-7 = 9x = 81° .
Now look at Angle-6 ... the one that's the answer to the problem.
Angle-6 and -7 together make a straight line, so they must
add up to 180°.
<u>Angle-6 + 81° = 180°</u>
Subtract 81° from each side: Angle-6 = <em>99° .</em>
